Ip address required?

Short answer: yes. :-)

Slightly less short answer: yes because they use two different ports. POP3 uses port 110 and SMTP uses port 25.

I would highly recommend being very comfortable with how the following work before attempting to setup your own mail server:

TCP Ports

SMTP

POP3

and last but not least:

Open relays

@untitled9:

and last but not least:

Open relays
Well put.

It's also a good idea to learn about SMTP AUTH and SSL.

If you can use an authenticated connection over an encrypted link, you don't have to worry about your ISP blocking port 25 (SMTP-over-SSL uses 465). Using POP3 or IMAP with SSL is also a win.

If you're only worried about providing service to yourself or a small group, you can make your own self-signed certificates (or, create your own Certificate Authority) and avoid forking over money to Verisign.